AH 3.3.4 The Superposition of Waves

Question 1

Explain what it means for two waves to be coherent.

Answer 1

Sources of waves are coherent if they have:

a) a constant phase relationship (i.e. are phase-linked)
b) have the same frequency

Question 2

Explain what is meant by

a) constructive interference (superposition)
b) destructive interference (superposition).

Answer 2

a) In constructive superposition two wave crests or troughs superpose exactly in phase to give a supercrest (maximum) or supertrough (minimum) respectively.
b) In destructive superposition a wave crest superposes exactly with a trough to create cancellation - a resultant wave of zero amplitude..

Question 3

a) What additional condition is required for two-source interference of visible light to occur?
b) How is this achieved in Young’s double slit interference experiment?
c) Draw a diagram of Young’s arrangement.

Answer 3

a) The two sources must receive their light from a point source (or at least a good approximation to it).
b) Light from an extended source (e.g. a bulb) is passed through a narrow single slit which acts as a point source for the two secondary sources.
c) See the diagram below - S_o acts as the point source.

Question 4

To produce a regular interference pattern for waves, what conditions must be met?

Answer 4

There must be two sources of waves which are

a) coherent
b) of the same amplitude

Question 5

Producing a regular two-source interference pattern for light waves is more difficult than for waves of longer wavelength e.g. microwaves.

a) Why is this?
b) What is done in practice to produce two-source interference with light waves?

Answer 5

a) The wavelength of visible light is so small that an extended source (one with measurable length, breadth and height like a bulb) must be regarded as a very large number of point sources. These point sources emit randomly and so will NOT be coherent.
b) Light from an extended source like a lamp is passed through a narrow single slit which acts as a single point source (or at least, a good approximation to it).

Light from this ‘point source’ may then be passed through two slits producing two secondary sources which are coherent.